The word toilet is actually a derivation from toilette which meant the refreshment, cleansing and dressing of the person. This included such activities as hair brushing and grooming, teeth brushing as well as application of make up, cleaning fingernails, etc., and generally attending to grooming of the person.
The lavatory is the recepticle in which a person passes water (urinates) or opens their bowels.
In England (as everywhere else) people have become lazy in their speech. One of the reasons why there is a degree of confusion is that many people used to ask to use a toilet, rather than a lavatory, as to ask to use a lavatory would be to acknowledge one needed to pass water of feaces which would have possibly caused embarrasment.
As lavatories were usually placed within, or close by, a toiletting area it was thought by many to avoid that embarrasment!
However in England we still call the soap we wash our hands, faces and bodies with, 'toilet soap'.
In well mannered and educated society these differences are still acknowledged and maintained.
The same applies to the difference between wash basins and sinks. A wash basin is only found in a toiletting area, for washing hands and face. A sink is only ever found in a kitchen or cooking area for the washing and rinsing of crockery, cutlery, food preparation or general domestic use.
Samantha